POTENTIAL FOR GENETIC SUPPRESSION OF INSECT POPULATIONS 



Total, where : is an arbitrary weighting 



factor : 



■ - y) dd males and females 



;. - i. y) DD males and females 



2 zxy (,..: - y) Dd males and females 



Similarly we might calculate the F2, F 3 . and 

 F, generations by determining what fraction of 

 each genotype from the previous generation 

 contributes to the current generation when all 

 combinations of the previous generation have 

 been determined. The following method de- 

 scribes our work with four genes and is gener- 

 ally applicable. All programs written for this 

 study had this same form. 



All possible genotypes will appear in the F 2 

 generation. Therefore the contribution by each 

 F; mating to a particular F 3 genotype will be the 

 same as the contribution from the same F3 mat- 

 ing to the same respective F^ genotype. This 

 holds true for all higher generations assuming 

 that no new genotypes are added and none of 

 the existing ones are removed. We have pro- 

 vided, a simplified block diagram of the general 

 program flow and the techniques employed in 

 developing computer programs suitable for this 

 study (fig. 1, Appendix). 



To make a computer program of this type 

 feasible, we first developed a unique numerical 

 representation for each genotype. Then we 

 developed a method to compute and store the 

 fractional contributions of all combinations of 

 Fi genotypes (i.e., matings) to each particular 

 member of the F 2 generation and the fractional 

 contributions of all combinations of F 2 geno- 

 types to each particular F 3 genotype. The con- 

 tributions of the latter remain constant for all 

 higher order cases. Therefore upon completion 

 of the Fa generation "formulas," the numerical 

 computations necessary to determine the final 

 answers can be made. We gave each allele a 

 unique number, and therefore we were able to 

 give each genotype a unique number. For exam- 

 ple, AaBbDdEe was assigned 12345678, and 

 A-BBDdee was assigned 10335688. The geno- 

 types with the exception of the Fi were gener- 

 ated by the computer. 



The first step in the program was to gener- 

 ate all possible genotypes that first appear in 

 the F 2 generation. Initially the genotypic identi- 

 fications for the Fi generation were read into 



the computer on punched cards. In handling the 

 identification, each group of eight numbers in 

 the case of four genes was treated as a set. Each 

 number, i.e., each allele, in the set was stored in 

 the core memory in such a way that it alone 

 could be available at any time. 



We generated the F 2 genotypes in the follow- 

 ing manner: The starting point in obtaining all 

 possible combinations of Fi genotypes was to 

 introduce two internal "pointers," Pi and P 2 , 

 with each pointer equal to 1. The genotypic 

 identification sets stored in the core memory in 

 locations relative to the pointer values were 

 then transferred to new core locations and ex- 

 panded into all possible combinations, taking 

 eight numbers at a time. Each combination was 

 stored immediately after its generation, and 

 thus upon completion of the expansion process, 

 256 new sets existed. This array then needed to 

 be searched to determine what genotypes had 

 been generated and what fractional contribu- 

 tion to the F 2 generation had been made. Each 

 number in the set of eight had a unique storage 

 location, but we needed to generate a single 

 identification number for each set (genotype). 

 This was accomplished by adding 1 to each mem- 

 ber of the set and then successively multiplying 

 the eight new numbers together. For example, 



storage appearance add 1, multiply 



12345678 

 result 



2X3X4X5X6X7X8X9 



362,880 



Since each identifier was unique, the result 

 after multiplication was unique. This result was 

 stored in one core location and thereby provided 

 an integer number for cross-reference to the 

 original alphabetical identification and also a 

 single number for future computations. We 

 then compiled a table 3 of these results. The 

 identification number of each set (genotype) 

 was compared with all existing identification 

 numbers in the table. If a matching number was 

 found, this meant that this particular genotype 

 had been previously generated and stored; if 

 not, the result was stored in the next available 

 position in the table. 



To determine what fractional contribution 



3 Refers to computer programing here and to dia- 

 gram of general program flow (fig. 1, Appendix), not 

 to text tables in this report. 



